화학공학소재연구정보센터
International Journal of Heat and Mass Transfer, Vol.76, 459-466, 2014
Elliptic formulation of the Simplified Spherical Harmonics Method in radiative heat transfer
The Simplified P-N-Approximation was introduced some 50 years ago, as an intuitive three-dimensional extension to the one-dimensional slab P-N-formulation. The set of simplified-P-N or SPN equations was formulated, such that they reduced to the standard P-N-approximation for a one-dimensional slab, resulting in 2(N + 1) simultaneous first order differential equations, subject to a modified set of Marshak boundary conditions. In this article the method is developed further for radiative heat transfer applications by reducing the governing equations to a small set of simultaneous second-order, elliptic PDEs, similar to the simple P-1 equation. Each of the equations is subject to P-1-type boundary conditions. Several two-dimensional examples are presented, including scattering, strongly inhomogeneous temperatures and absorption coefficients. (C) 2014 Elsevier Ltd. All rights reserved.